TSTP Solution File: CAT014-4 by Prover9---1109a
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- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : CAT014-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 00:06:17 EDT 2022
% Result : Unsatisfiable 0.44s 1.04s
% Output : Refutation 0.44s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT014-4 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : tptp2X_and_run_prover9 %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 17:49:11 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.44/1.04 ============================== Prover9 ===============================
% 0.44/1.04 Prover9 (32) version 2009-11A, November 2009.
% 0.44/1.04 Process 6692 was started by sandbox2 on n025.cluster.edu,
% 0.44/1.04 Sun May 29 17:49:12 2022
% 0.44/1.04 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_6538_n025.cluster.edu".
% 0.44/1.04 ============================== end of head ===========================
% 0.44/1.04
% 0.44/1.04 ============================== INPUT =================================
% 0.44/1.04
% 0.44/1.04 % Reading from file /tmp/Prover9_6538_n025.cluster.edu
% 0.44/1.04
% 0.44/1.04 set(prolog_style_variables).
% 0.44/1.04 set(auto2).
% 0.44/1.04 % set(auto2) -> set(auto).
% 0.44/1.04 % set(auto) -> set(auto_inference).
% 0.44/1.04 % set(auto) -> set(auto_setup).
% 0.44/1.04 % set(auto_setup) -> set(predicate_elim).
% 0.44/1.04 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.44/1.04 % set(auto) -> set(auto_limits).
% 0.44/1.04 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.44/1.04 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.44/1.04 % set(auto) -> set(auto_denials).
% 0.44/1.04 % set(auto) -> set(auto_process).
% 0.44/1.04 % set(auto2) -> assign(new_constants, 1).
% 0.44/1.04 % set(auto2) -> assign(fold_denial_max, 3).
% 0.44/1.04 % set(auto2) -> assign(max_weight, "200.000").
% 0.44/1.04 % set(auto2) -> assign(max_hours, 1).
% 0.44/1.04 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.44/1.04 % set(auto2) -> assign(max_seconds, 0).
% 0.44/1.04 % set(auto2) -> assign(max_minutes, 5).
% 0.44/1.04 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.44/1.04 % set(auto2) -> set(sort_initial_sos).
% 0.44/1.04 % set(auto2) -> assign(sos_limit, -1).
% 0.44/1.04 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.44/1.04 % set(auto2) -> assign(max_megs, 400).
% 0.44/1.04 % set(auto2) -> assign(stats, some).
% 0.44/1.04 % set(auto2) -> clear(echo_input).
% 0.44/1.04 % set(auto2) -> set(quiet).
% 0.44/1.04 % set(auto2) -> clear(print_initial_clauses).
% 0.44/1.04 % set(auto2) -> clear(print_given).
% 0.44/1.04 assign(lrs_ticks,-1).
% 0.44/1.04 assign(sos_limit,10000).
% 0.44/1.04 assign(order,kbo).
% 0.44/1.04 set(lex_order_vars).
% 0.44/1.04 clear(print_given).
% 0.44/1.04
% 0.44/1.04 % formulas(sos). % not echoed (13 formulas)
% 0.44/1.04
% 0.44/1.04 ============================== end of input ==========================
% 0.44/1.04
% 0.44/1.04 % From the command line: assign(max_seconds, 300).
% 0.44/1.04
% 0.44/1.04 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.44/1.04
% 0.44/1.04 % Formulas that are not ordinary clauses:
% 0.44/1.04
% 0.44/1.04 ============================== end of process non-clausal formulas ===
% 0.44/1.04
% 0.44/1.04 ============================== PROCESS INITIAL CLAUSES ===============
% 0.44/1.04
% 0.44/1.04 ============================== PREDICATE ELIMINATION =================
% 0.44/1.04 1 -there_exists(A) | A != B | equivalent(A,B) # label(existence_and_equality_implies_equivalence1) # label(axiom). [assumption].
% 0.44/1.04 2 -equivalent(A,B) | there_exists(A) # label(equivalence_implies_existence1) # label(axiom). [assumption].
% 0.44/1.04 3 -equivalent(A,B) | A = B # label(equivalence_implies_existence2) # label(axiom). [assumption].
% 0.44/1.04
% 0.44/1.04 ============================== end predicate elimination =============
% 0.44/1.04
% 0.44/1.04 Auto_denials:
% 0.44/1.04 % copying label prove_codomain_is_idempotent to answer in negative clause
% 0.44/1.04
% 0.44/1.04 Term ordering decisions:
% 0.44/1.04 Function symbol KB weights: a=1. compose=1. domain=1. codomain=1.
% 0.44/1.04
% 0.44/1.04 ============================== end of process initial clauses ========
% 0.44/1.04
% 0.44/1.04 ============================== CLAUSES FOR SEARCH ====================
% 0.44/1.04
% 0.44/1.04 ============================== end of clauses for search =============
% 0.44/1.04
% 0.44/1.04 ============================== SEARCH ================================
% 0.44/1.04
% 0.44/1.04 % Starting search at 0.01 seconds.
% 0.44/1.04
% 0.44/1.04 ============================== PROOF =================================
% 0.44/1.04 % SZS status Unsatisfiable
% 0.44/1.04 % SZS output start Refutation
% 0.44/1.04
% 0.44/1.04 % Proof 1 at 0.02 (+ 0.00) seconds: prove_codomain_is_idempotent.
% 0.44/1.04 % Length of proof is 20.
% 0.44/1.04 % Level of proof is 6.
% 0.44/1.04 % Maximum clause weight is 12.000.
% 0.44/1.04 % Given clauses 37.
% 0.44/1.04
% 0.44/1.04 4 there_exists(codomain(a)) # label(assume_codomain_exists) # label(hypothesis). [assumption].
% 0.44/1.04 5 compose(A,domain(A)) = A # label(compose_domain) # label(axiom). [assumption].
% 0.44/1.04 6 compose(codomain(A),A) = A # label(compose_codomain) # label(axiom). [assumption].
% 0.44/1.04 9 codomain(codomain(a)) != codomain(a) # label(prove_codomain_is_idempotent) # label(negated_conjecture) # answer(prove_codomain_is_idempotent). [assumption].
% 0.44/1.04 11 -there_exists(codomain(A)) | there_exists(A) # label(codomain_has_elements) # label(axiom). [assumption].
% 0.44/1.04 12 -there_exists(compose(A,B)) | there_exists(domain(A)) # label(composition_implies_domain) # label(axiom). [assumption].
% 0.44/1.04 13 -there_exists(compose(A,B)) | domain(A) = codomain(B) # label(domain_codomain_composition1) # label(axiom). [assumption].
% 0.44/1.04 14 -there_exists(compose(A,B)) | codomain(B) = domain(A). [copy(13),flip(b)].
% 0.44/1.04 17 codomain(codomain(a)) = c_0. [new_symbol(9)].
% 0.44/1.04 18 codomain(a) != c_0 # answer(prove_codomain_is_idempotent). [back_rewrite(9),rewrite([17(3)]),flip(a)].
% 0.44/1.04 22 there_exists(a). [hyper(11,a,4,a)].
% 0.44/1.04 23 -there_exists(A) | there_exists(domain(A)). [para(5(a,1),12(a,1))].
% 0.44/1.04 26 -there_exists(A) | codomain(domain(A)) = domain(A). [para(5(a,1),14(a,1))].
% 0.44/1.04 27 -there_exists(A) | domain(codomain(A)) = codomain(A). [para(6(a,1),14(a,1)),flip(b)].
% 0.44/1.04 34 there_exists(domain(codomain(a))). [hyper(23,a,4,a)].
% 0.44/1.04 36 there_exists(domain(domain(codomain(a)))). [hyper(23,a,34,a)].
% 0.44/1.04 85 codomain(domain(domain(domain(codomain(a))))) = domain(domain(domain(codomain(a)))). [hyper(26,a,36,a)].
% 0.44/1.04 115 domain(codomain(a)) = codomain(a). [hyper(27,a,22,a)].
% 0.44/1.04 121 codomain(a) = c_0. [back_rewrite(85),rewrite([115(3),115(3),115(3),17(3),115(4),115(4),115(4)]),flip(a)].
% 0.44/1.04 122 $F # answer(prove_codomain_is_idempotent). [resolve(121,a,18,a)].
% 0.44/1.04
% 0.44/1.04 % SZS output end Refutation
% 0.44/1.04 ============================== end of proof ==========================
% 0.44/1.04
% 0.44/1.04 ============================== STATISTICS ============================
% 0.44/1.04
% 0.44/1.04 Given=37. Generated=243. Kept=115. proofs=1.
% 0.44/1.04 Usable=29. Sos=31. Demods=37. Limbo=10, Disabled=57. Hints=0.
% 0.44/1.04 Megabytes=0.10.
% 0.44/1.04 User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
% 0.44/1.04
% 0.44/1.04 ============================== end of statistics =====================
% 0.44/1.04
% 0.44/1.04 ============================== end of search =========================
% 0.44/1.04
% 0.44/1.04 THEOREM PROVED
% 0.44/1.04 % SZS status Unsatisfiable
% 0.44/1.04
% 0.44/1.04 Exiting with 1 proof.
% 0.44/1.04
% 0.44/1.04 Process 6692 exit (max_proofs) Sun May 29 17:49:12 2022
% 0.44/1.04 Prover9 interrupted
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